Key points are not available for this paper at this time.
In 1996 Erdős showed that among planar domains of fixed area, the smallest principal eigenvalue of the Dirichlet Laplacian with a constant magnetic field is uniquely achieved on the disk. We establish a quantitative version of this inequality, with an explicit remainder term depending on the field strength that measures how much the domain deviates from the disk.
Ghanta et al. (Wed,) studied this question.